Question

the image of the point $(-5,-5)$ under a translation is $(0,0)$. find the coordinates of the image of the point $(9,4)$ under the same translation.

Explanation:

Step1: Find the translation rule

Let the translation be \((x,y)\to(x + a,y + b)\).
Given \((-5,-5)\to(0,0)\), so \(-5+a = 0\) and \(-5 + b=0\).
Solving \(-5+a = 0\) gives \(a=5\). Solving \(-5 + b=0\) gives \(b = 5\). The translation rule is \((x,y)\to(x + 5,y + 5)\).

Step2: Apply the translation rule to the point \((9,4)\)

For the point \((9,4)\), \(x=9\) and \(y = 4\).
Using the rule \(x+5=9 + 5=14\) and \(y+5=4 + 5=9\).

Answer:

$(14,9)$